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Uncategorized » The Calculating Investor » Page 4

A Reading List for Analytical Investors

I enjoy working with investment simulations and models, and this reading list is for investors who want to learn do their own investment analysis.

All of the books on this list require a fair amount of math, but I have labeled a few books which are especially challenging as “Advanced”.

For investors who want to learn about investing without all the mathematics, models, and spreadsheets, I recommend checking out my “Part 1” list.

  • The Intelligent Asset Allocator – William Bernstein:  This book is a basic introduction to portfolio theory and asset allocation.  The book walks the reader though the valuable concept of mean-variance optimization, and it has great chapters on market efficiency and on constructing your personal portfolio.
  • An R Companion to Applied Regression – John Fox:  This book has nothing to do with investing or finance, but it does provide an excellent introduction to the R programming language.  R is a sophisticated statistical analysis software package which is open source and available for free.  I frequently use R for the regression analysis and simulations on this website.
  • Valuation – Koller, Goedhart, and Wessels:  This book is about valuing companies.  I’m not a fan of picking individual stocks for my investment portfolio, so this might seem like an odd recommendation.  However, I think valuation is a fascinating topic.  I used this book as part of a Financial Statement Analysis class at the University of Chicago, and I liked it because it goes beyond the mechanics of valuation and forces you to think hard about the inputs used in the models.   I think some understanding of stock valuation is important..even for a diehard indexer such as myself.
  • Active Portfolio Management – Grinold and Kahn (Advanced): As the title suggests, this book is about using quantitative techniques to actively manage a portfolio.  This book is geared towards practitioners, but it does have some heavy duty math.  I like this book because it provides very clear explanations for many of the important ideas in quantitative finance.  It covers asset pricing models, risk, expected returns, valuation, forecasting, etc.  Also, there is an interesting chapter on the historical record of active management.  I’m going to stick with indexing, but it is interesting to hear the case for active management presented by sophisticated investors who are familiar with the academic evidence against it.
  • Derivatives Markets – Robert L. McDonald (Advanced): This is a textbook on financial instruments.  Futures, swaps, and options are covered in detail.  I don’t use any of these instruments in my own portfolio, and I think individual investors who do use them are usually using them for speculation.  Nevertheless, these instruments play an important role in modern financial markets, and they can help individuals and institutions to manage risk in some situations.
  • Asset Pricing – John H. Cochrane (Advanced):  One of the reviews for this book on Amazon is titled “Not for Wimps”.  I agree with that description.  The book starts out with a derivation of a consumption based model of asset pricing, and the rest of the book builds from that foundation.  The book is theoretical, and it lacks the “how-to” examples of more basic books.  However, if you really want to develop a deep understanding of asset pricing theory, then this is a great book. 

Disclosure: The links in this post are affiliate links. That means that if you click through from my link and buy the book, I receive a small commission.

Why I am skeptical about the “rebalancing bonus” even though I believe that “buy, hold, and rebalance” is a great investment strategy

This past week, Rick Ferri, the Founder of Portfolio Solutions, wrote an interesting blog post on Forbes.com titled “Passive Investing Beats the Markets”. In the post, Mr. Ferri argues that a buy, hold, and rebalance strategy using low cost index funds outperforms a number of other strategies including an index-based strategy of buy, hold, and never rebalance.

In a related discussion on Bogleheads.org, Mr. Ferri provided some historical data supporting this conclusion, but I thought I would take a stab at running some simulations to better understand the conditions where rebalancing can boost total returns.

The Bernstein Analysis of the Rebalancing Bonus

In 1997, William Bernstein published an analysis on his website which showed how the “rebalancing bonus” was affected by the difference in average returns between two securities and the correlation between those returns.

Bernstein’s analysis showed that rebalancing can increase returns when two volatile securities have similar average returns and low correlation. The intuition behind this result is straighforward, if two securities are highly correlated, then there is little opportunity to transfer funds from the security which is performing relatively well to the security that is performing relatively poorly. If the securities have low correlation, then there are more frequent opportunities to “buy low, sell high” through rebalancing.

Similarly, if the two securities have very different average returns, then the rebalancing will, on average, move funds from the security with higher average returns to the security with lower average returns. This is obviously not a strategy which will boost total returns over time, although it may make sense for risk management purposes.

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Robert Merton Discusses a Framework for Improving Defined Contribution Plans

The MIT World website is a great source for interesting lectures on many topics including finance and economics.  In this lecture, Nobel Laureate Robert Merton discusses a framework for the defined contribution (DC) plan of the future.

This video includes a long introduction, and Merton makes some opening remarks about the financial crisis.  His discussion of retirement plans starts about 17 minutes into the presentation.

Merton suggests that the DC plan of the future should require investors to make three simple decisions which will in turn drive the investment choices which are made (for them) within their portfolio. The three “sliders” which investors can adjust to control the decisions made in their portfolios are contribution level, number of working years, and minimum acceptable retirement income (i.e. a risk adjustment).

An interesting take-away from the presentation is Merton’s suggestion that risk be evaluated in terms of an asset’s volatility when valued in “annuity units”. Merton’s point is that many investments we perceive as “safe” would appear less safe if we translated them in the units that really matter…i.e. how much are they worth in terms of income at retirement.

I am not completely sold on Merton’s plan because, as a “do it yourself” investor, I don’t want to lose control of my investment decisions.  Also, I don’t trust that the money management industry will provide a solution which keeps costs low.  Nevertheless, it is interesting to see how Merton frames the retirement problem, and I would be very interested to see some portfolio construction tools which determine an asset allocation based on the three inputs he proposes.

For those interested in this topic, here is an article written by Merton which covers some similar ground.

Two Common Questions

Over the past few weeks, gasoline prices have been a frequent conversation topic. The rapid rise in prices has hit most of us in the pocketbook, and it has caused wannabe economists such as myself to ponder the relationship between oil and gasoline prices.

In this post, I’m going to look at two common questions to see if we can reach any conclusions.

Question #1: What is the relationship between Oil Prices and Gasoline Prices?

This is a relatively easy question to answer. The data on oil prices is available on the EIA website, and the same website has data on retail gasoline prices for a variety of cities and regions. Since I am a Chicago resident, I chose to run the regression using the retail gasoline price series for Chicago.

This plot shows the last seven years of oil and gasoline prices. The blue dots are the weekly price data points and the red line is the fitted regression line.

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A Reading List for Individual Investors

I enjoy reading about investing, and, over the years, I have built up quite a large library of investing books. I thought I’d share a few of my favorites.

Readers may notice that the books I’ve listed cover several different investment philosophies. I’m an advocate of indexing, but I have included one “stock picking” classic (The Intelligent Investor). I’ve also included several books on behavioral finance. I think it is important for investors to be exposed to a variety of viewpoints, and I believe that each of these books contains some valuable wisdom.

I have labeled this list as “Part 1” because I plan to follow-up in a week or two with another list which focuses more on the analytics of investing. The “Part 2” list will include textbook and “how-to” book suggestions.

  1. Common Sense on Mutual Funds – John C. Bogle:  This is a must read for every investor.  The book makes an excellent case for indexing.  Regardless of your investing philosophy, you should read this book and think hard about Bogle’s arguments.
  2. Unconventional Success – David F. Swensen: Swensen is the manager of Yale University’s endowment.  This book is geared towards individual investors (he has another book aimed at institutional money managers), and it is entertaining and informative to read Swensen’s attacks on much of the money management industry.  Before I read this book, I was unaware of many of the sneaky methods which are used to hide fees within actively managed funds.
  3. A Random Walk Down Wall Street – Burton G. Malkiel: I haven’t read the latest edition of this book, but this is an investing classic.  The book advocates indexing and intelligent asset allocation.
  4. Stocks for the Long Run – Jeremy J. Siegel: Siegel is typically very optimistic about the future of equities, and, in this book, he makes his case using a tremendous amount of historical data.  This is another book where I haven’t read the latest edition.  I have read that he recommends overweighting dividend stocks in this edition. I’m not sure I would agree, but I’d love to read the argument and see the data.  Continue reading »

Can investors reliably pick mutual funds which beat the market?

I am a very big fan of index funds. However, I often hear the argument from my friends and relatives that index investors are content to be “average” and that smart investors who are well informed and willing to put in a little extra work should be able to “beat the market”.

If only it were that easy! There are numerous academic studies showing that, after fees, the average active mutual fund underperforms low cost index funds. These studies also show that there is very little “persistence” among the mutual funds that have managed to beat the indexes in the past. In other words, we can’t accurately predict which funds which will beat the market in the future by looking at past performance.

Despite all the evidence in favor of index funds, I find that it is very difficult to change the mind of a diehard believer in active management. Instead, I choose to stress the importance of carefully measuring investment performance. I strongly believe that any investor who does not carefully measure and evaluate investment performance is not a serious investor!  I have found that most investors who carefully and honestly monitor the performance of their investments and compare this performance to a relevant benchmark will eventually convince themselves that indexing is the way to go. Continue reading »

I’m a financial data junkie, so I thought I’d share some of my favorite sites for free financal and economic data.  I’ve also added links to these sites to the sidebar, and I’ll keep the sidebar list updated as I find new data sources.

  • Yahoo! Finance:  Yahoo! Finance is a great site for ETF, mutual fund, and stock data.  The site allows historical price data to be downloaded in a CSV format, and this makes it easy to calculate historical returns.  For example, the R-script I created for calculating Fama-French factor loading automatically downloads the CSV file for the target fund and converts the price data to a monthly return series..
  • Google Finance:  Google Finance is similar to Yahoo! Finance, but it lacks the historical dividend information.  This makes it less useful for analyzing historical returns.  However, Google Docs provides a “GoogleFinance” function which allows stock or fund information to be downloaded directly into a Google Docs Spreadsheet.  This is a great feature which makes it easy to setup a spreadsheet to track your portfolio.  It is possible to directly download stock information from Yahoo! Finance into Excel, but the Google Docs + Google Finance combination makes it easy.
  • Fama-French Data Library:  This site has a large amount of historical data compiled by Eugene Fama and Kenneth French.  The data is updated regularly, and the Fama-French 3-factor data is especially useful for analyzing fund and portfolio performance.
  • Robert Shiller PE10 Data: This site has Robert Shiller’s PE10 data which was used in the book “Irrational Exuberance”.   I used this data to create a regression model for forecasting future returns.  Shiller’s PE10 data is also updated regularly.
  • Federal Reserve Economic Data (FRED):  This site has a wide variety of macroeconomic data including data for unemployment, GDP, interest rates, the money supply, etc.   The site also has pretty good tools for plotting the data.
  • Treasury Yield Curve Rates: This site has historical and current data for the Treasury and TIPS yield curves.  I previously posted an Octave script which uses this data to calculate inflation expectations.
  • Statistical Abstract of the United States:  This site has a variety of U.S. and International Economic data.  I think the data on foreign stock market capitalization is especially interesting and I’m hoping to work this into a future post.

Monte Carlo Simulations using return data from 1926-2010

In 1975, Nobel laureate William Sharpe published a study titled “Likely Gains from Market Timing”. In this paper, Sharpe reportedly found that a market timer who switches between 100% stocks and 100% T-bills on an annual basis must be correct about 74% of the time (on average) to beat the market.

Unfortunately, a free copy of this paper is not available on the web, and I don’t have access to this much cited paper. However, I’ve seen a number of related analyses based on Sharpe’s approach, and I believe we can recreate a similar result through simulation.

In this post, I’ll simulate a simple market timing strategy and determine the market timing accuracy required to outperform buy-and-hold. I’ll compare market timing to buy-and-hold in terms of both total returns and risk-adjusted returns (measured by the Sharpe Ratio). I’m going to use market and T-bill returns for the years 1927-2010.

My assumptions are that an investor makes a decision at the beginning of each year to invest in either stocks or T-bills, based on his/her prediction for the coming year. The Monte Carlo simulation is run using the actual annual returns for stocks and T-bills from 1927 to 2010, and 10,000 runs of the simulation are plotted to generate a distribution.

The Monte-Carlo results for 50% prediction accuracy are shown below.  The red line represents the arithmetic average return for a buy and hold investor over the years from 1926 thru 2010, and the distribution represents the market timing outcomes for the 10,000 trials:

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How confident should you be about your investment goals?

What is the probability that your investments will fall short of a particular investment goal?  How is this probability affected by uncertainty about the equity risk premium?

In this post, I plan to look at a simple method for estimating the probability that a risky investment will fall short of a particular return goal, and I’ll then extend this analysis to allow for uncertainty about the equity risk premium.

This analysis is a very simplified example of the concept presented by Lubos Pastor and Robert F. Stambaugh in their paper “Are Stocks Really Less Volatile in the Long Run?”.

For starters, if we assume stock prices follow a random walk, then the probability of a risky investment underperforming a risk free investment, such as a T-bill, is given by this equation:

 Shortfall Probability = Prob\left ( z< \sqrt{T} \frac{r-\mu }{\sigma }\right )

r = continuously compounded (log return) t-bill rate
\mu = continuously compounded (log) equity return
\sigma = annual standard deviation of equity returns
T = number of years

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So far, so good, but the debate is not over…and may not be for a while

In late 2005, PowerShares launched an ETF (ticker symbol: PRF) based on a controversial new “index” known as the Research Affiliates Fundamental 1000 Index (RAFI 1000).   We now have over 5 years of return data for this fund, and this seems to me to be enough data for us to take a preliminary look at the strategy’s performance. 

A quick comparison of PRF against popular traditional index funds such as SPY and VTI is shown below.  This plot shows total returns (including dividends).

This graph shows that PRF has outperformed both SPY and VTI over the past 5 years, but it also experienced a larger drop during the crisis of 2008 and 2009.  To properly evaluate the performance of PRF, we need adjust the returns for risk using an asset pricing model such as the Fama-French Three Factor Model (FF3F).  However, before I get to the detailed analysis, I’d like to review what Fundamental Indexing is and why it is controversial.

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